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Spatiotemporal Signature Vectors and Entanglement Networks: From Scalar Bell Tests to Event-Level Quantum Diagnostics

Hema Kasisomayajula

Published Jan 1, 2026• 0 citations
Publisher

Abstract

This work introduces the concept of spatiotemporal signatures (Σ) as a diagnostic layer for analyzing quantum entanglement. By retaining and quantifying temporal and spatial correlations from raw CHSH-type coincidence datasets, Σ captures structure beyond conventional Bell statistics. Using Σ-distance graphs, we demonstrate how Bell-identical experiments can separate into distinct clusters, revealing entanglement networks whose membership is defined by shared correlation properties rather than time or space. The framework enables network-level metrics such as coherence, diameter, and membership entropy, and naturally connects to quantum repeaters, satellite-based entanglement distribution, and emerging quantum internet architectures. This approach is designed to augment traditional entanglement certification without altering its theoretical foundations, providing a scalable and operational method for characterizing multipartite and distributed quantum correlations.

DOI
10.17605/osf.io/9md6e

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This work introduces the concept of spatiotemporal signatures (Σ) as a diagnostic layer for analyzing quantum entanglement. By retaining and quantifying temporal and spatial correlations from raw CHSH-type coincidence datasets, Σ captures structure beyond conventional Bell statistics. Using Σ-distance graphs, we demonstrate how Bell-identical experiments can separate into distinct clusters, revealing entanglement networks whose membership is defined by shared correlation properties rather than time or space. The framework enables network-level metrics such as coherence, diameter, and membership entropy, and naturally connects to quantum repeaters, satellite-based entanglement distribution, and emerging quantum internet architectures. This approach is designed to augment traditional entanglement certification without altering its theoretical foundations, providing a scalable and operational method for characterizing multipartite and distributed quantum correlations.
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The notion of a spatiotemporal quantum state extends the conventional concept of a spatial quantum state to the spatiotemporal domain. Such states are represented by unit-trace operators that encode correlations among quantum events distributed across space and time. In this work, we use the spatiotemporal Kirkwood-Dirac phase space to provide a unified characterization of spatiotemporal quantum states. Spatiotemporal states obtained from Kirkwood-Dirac distributions are generally non-Hermitian and nonnormal; whereas those constructed from Margenau-Hill distributions are Hermitian. We provide a unification via (quasi)probabilistic mixture of Kirkwwod-Dirac spatiotemporal states which encompasses almost all existing formulations of spatiotemporal quantum states. We derive recursive expressions for spatiotemporal states and elucidate the relation between Kirkwood-Dirac nonclassicality and the temporality of spatiotemporal states. We further extend the construction to many-fold correlation functions and establish its connection with out-of-time-ordered correlators (OTOCs). We also develop a more general unifying framework based on (quasi)probabilistic mixture of sss-parametrized spatiotemporal states and establish their Petz time reversal and application in studying Kubo-Martin-Schwinger (KMS) condition in two-time setting. Finally, we apply this framework to characterize quantum entanglement in spacetime and analyze spatiotemporal entanglement using several complementary entropy measures.
Quantum entanglement, a cornerstone of quantum mechanics, presents a profound challenge to our understanding of measurement and information. Traditional methods of quantifying entanglement, such as correlation measurements, often fail to capture the subtle nuances and interconnectedness of these fundamental phenomena. This paper introduces a novel metric, the 'Entanglement Flow,' designed to quantify the distance between entangled quantum systems, leveraging principles from quantum information theory and incorporating non-classical entanglement properties. The core mechanism centers on the concept of an entanglement flow, which dynamically tracks the evolution of entanglement across a system, providing a quantifiable measure of its connectedness. This approach moves beyond simple correlation analysis and offers a more sophisticated framework for characterizing the robustness and nature of quantum correlations. We demonstrate the effectiveness of this metric through rigorous theoretical analysis and preliminary experimental validation, suggesting it has the potential to significantly advance our comprehension of entanglement dynamics.
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Quantum entanglement is a non-classical correlation between quantum systems that cannot be accounted for by any local hidden-variable theory. Since its articulation in the Einstein-Podolsky-Rosen paper of 1935 and its formal testability through Bell's theorem in 1964, entanglement has evolved from a philosophical puzzle into the central resource of quantum information science. This review surveys the conceptual foundations of entanglement, the experimental record culminating in loophole-free Bell tests, and applications including quantum key distribution, quantum teleportation, and measurement-based quantum computation. We summarise quantitative results of representative Bell experiments, discuss entanglement measures for mixed states, and outline recent developments in long-distance entanglement distribution via satellites and quantum repeaters. Persistent challenges decoherence, certification of high-dimensional entanglement, and scalable distribution are identified as active frontiers of research.
The two-state-vector formalism and the entangled histories formalism are attempts to better understand quantum correlations in time. Both formalisms share some similarities, but they are not identical, having subtle differences in their interpretation and manipulation of quantum temporal structures. However, the main objective of this paper is to prove that, with appropriately defined scalar products, both formalisms can be made isomorphic. We show, for instance, that they treat operators and states on equal footing, leading to the same statistics for all measurements. In particular, we discuss the topic of quantum correlations in time and show how they can be generated and analyzed in a consistent way using these formalisms. Furthermore, we elaborate on an unconventional behavior of quantum histories of evolving multipartite systems which do not exhibit global nonlocal correlations in time but nevertheless can lead to entangled reduced histories characterizing evolution of an arbitrarily chosen subsystem.